Introduction to Automata Theory, Languages, and Computation
Introduction to Automata Theory, Languages, and Computation Free Course in Automata Theory I have prepared a course in automata theory (finite automata, context-free grammars, decidability, and intractability), and it begins April 23, 2012. You can learn more about the course at www.coursera.org/course/automata. Several other courses will start at the same time, including Alex Aiken on Compilers,
はじめての圏論 その第1歩：しりとりの圏 - 檜山正幸のキマイラ飼育記
全体目次： 第1歩：しりとりの圏 （このエントリー） 第2歩：行列の圏 第3歩：極端な圏達 第4歩：部分圏 第5歩：変換キューの圏 第6歩：有限変換キューと半圏 第7歩：アミダの圏 第8歩：順序集合の埋め込み表現 第9歩：基本に戻って、圏論感覚を養うハナシとか 付録／番外など： 中間付録A：絵を描いてみた 番外：同期／非同期の結合 中間付録B：アミダとブレイド 番外：米田の補題に向けてのオシャベリ 一部のプログラミング言語の背景として、圏論（カテゴリー論）が使われたりするせいか、以前に比べれば多少は圏論に興味を持つ人が増えたような気がしなくもないような。でも、安直な入門的文書はあまり見かけないですね。もちろん、シッカリした教科書や論説はあるんですが、どうもシッカリし過ぎているような。例えば、圏の例として「コンパクト・ハウスドルフ空間と連続写像の圏」とか言われてもねぇ（この例はいい例なんです
Order theory - Wikipedia
This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (December 2015) (Learn how and when to remove this template message) Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for d
Denotational semantics - Wikipedia
In computer science, denotational semantics (initially known as mathematical semantics or Scott–Strachey semantics) is an approach of formalizing the meanings of programming languages by constructing mathematical objects (called denotations) that describe the meanings of expressions from the languages. Other approaches providing formal semantics of programming languages include axiomatic semantics
Mathematical logic - Wikipedia
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize c
Propositional calculus - Wikipedia
Although propositional logic (which is interchangeable with propositional calculus) had been hinted by earlier philosophers, it was developed into a formal logic (Stoic logic) by Chrysippus in the 3rd century BC[2] and expanded by his successor Stoics. The logic was focused on propositions. This advancement was different from the traditional syllogistic logic, which was focused on terms. However,
Computability theory - Wikipedia
Computability theory originated in the 1930s, with the work of Kurt Gödel, Alonzo Church, Rózsa Péter, Alan Turing, Stephen Kleene, and Emil Post.[2][nb 1] The fundamental results the researchers obtained established Turing computability as the correct formalization of the informal idea of effective calculation. In 1952, these results led Kleene to coin the two names "Church's thesis"[3]: 300 and
Zermelo–Fraenkel set theory - Wikipedia
In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic
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ホクト・システム ちょっといい話 有限要素法・よもやま話「第1話 ＬとＧ − 数学者群像」
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First-order logic - Wikipedia